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Aside from the common usage of the term 'potential,' was the development of the idea of potential energy influenced by the Aristotelian idea of potentiality and actuality, at least historically?

Newtonian mechanics was developed right after the medieval period which was heavily influenced by Aristotelian metaphysics.

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Yes, obviously.

The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine.

As you can see from Rankine's 1853 original paper, the author speaks of Actual energy and Potential energy.

But note that "potential energy" is not a Newtonian term : the concept of energy is not present in Newton's works.

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Heisenberg wrote in his Physics and Philosophy p. 42 that the probability wave concept in quantum mechanics

was a quantitative version of the concept of "potentia" in Aristotelian philosophy.

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